Set-Theoretic and Algebraic Structures for Sensory Research

Sensory research is often organized around receptor mechanisms, physical stimulus variables, numerical intensity scales, neural correlates, or linguistic reports. These approaches are indispensable, but they do not by themselves provide a general method for comparing the structured sensory worlds of different subjects. This paper proposes a set-theoretic and algebraic framework in which a sensory system is represented as a subject-relative structured set consisting of sensory classes, distinguished subsets, relations, partial operations, and context-dependent transformations. A translation between two sensory systems is not defined as identity of internal experience or as a mere correspondence between labels. It is defined as a partial relation or partial map that preserves specified structural features on a restricted domain. Taste is used as the primary case. The framework distinguishes intensity from classification boundaries, similarity, ordering, incompatibility, mixture, aftertaste, temporal order, temperature dependence, and cross-modal interaction. It supports a staged medical-AI architecture in which population data yield a finite library of sensory phenotypes, a patient is first represented as a mixture of those phenotypes, and individual residual corrections are learned from limited personal data. Such a system could simulate how foods, medicines, treatments, or sensory-substitution devices may be experienced by a patient or by a clinically relevant sensory type. The same mathematics supports artificial sensory languages, translated animal reports such as a structurally grounded ``cat food review,'' and synesthesia as partial translation between distinct sensory structures within one subject. The framework neither assumes nor denies the existence of qualia in humans, animals, or artificial systems. Because qualia are not directly available as intersubjectively observable data, they are not used as a direct success criterion. Nevertheless, stable differences in subject-relative sensory structures may serve as indirect structural indicators of differences in experience. This paper is conceptual and methodological: it defines the mathematical objects, translation criteria, empirical construction procedures, and research program, without claiming that the proposed translations have already been experimentally established.